\documentclass{article}
\usepackage{iftex}
\usepackage{ifthen}
\usepackage{epsfig}
\usepackage[utf8]{inputenc}
\usepackage{xcolor}
\ifPDFTeX
\usepackage{newunicodechar}
  \makeatletter
    \def\doxynewunicodechar#1#2{%
    \@tempswafalse
    \edef\nuc@tempa{\detokenize{#1}}%
    \if\relax\nuc@tempa\relax
      \nuc@emptyargerr
    \else
      \edef\@tempb{\expandafter\@car\nuc@tempa\@nil}%
      \nuc@check
      \if@tempswa
        \@namedef{u8:\nuc@tempa}{#2}%
      \fi
    \fi
  }
  \makeatother
  \doxynewunicodechar{⁻}{${}^{-}$}% Superscript minus
  \doxynewunicodechar{²}{${}^{2}$}% Superscript two
  \doxynewunicodechar{³}{${}^{3}$}% Superscript three

\fi
\pagestyle{empty}
\begin{document}
$\epsilon=1\times10^{-12}$
\pagebreak

\[
         v_t = \beta v_{t-1} + (1 - \beta) g_t^2
         \]
\pagebreak

\[
         \theta_t = \theta_{t-1} - \frac{\eta}{\sqrt{v_t + \epsilon}} g_t
         \]
\pagebreak

\end{document}
